Let $a_1;a_2;\cdots;a_n;b_1;b_2;\cdots;b_n$ be positive numbers. Prove that at least one of the following must be true,
\[\frac{a_1}{b_1} + \frac{a_2}{b_2} + \cdots + \frac{a_n}{b_n} \geq n\]
\[\frac{b_1}{a_1} + \frac{b_2}{a_2} + \cdots + \frac{b_n}{a_n} \geq n\]
Camp exam problem 7
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Nur Muhammad Shafiullah | Mahi
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Nur Muhammad Shafiullah | Mahi
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nafistiham
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Re: Camp exam problem 7
again, simple AM-GM
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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Tahmid Hasan
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Re: Camp exam problem 7
Please post the solution because I can't solve it. 
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